Abstract: Let be an excellent local ring of positive prime characteristic. We show that if , then is regular. This improves a result of Schoutens, in which the additional hypothesis that was an isolated singularity was required for the proof.

5.Craig
Huneke, Tight closure and its applications, CBMS Regional
Conference Series in Mathematics, vol. 88, Published for the
Conference Board of the Mathematical Sciences, Washington, DC; by the
American Mathematical Society, Providence, RI, 1996. With an appendix by
Melvin Hochster. MR
1377268

Craig Huneke, Tight closure and its applications, With an appendix by Melvin Hochster. CBMS Regional Conference Series in Mathematics, 88. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1996. x+137 pp. ISBN: 0-8218-0412-X. MR 96m:13001